A small circle fits between two touching circles so that all three
circles touch each other and have a common tangent? What is the
exact radius of the smallest circle?
Given any three non intersecting circles in the plane find another
circle or straight line which cuts all three circles orthogonally.
Here is a pattern for you to experiment with using graph drawing
software. Find the equations of the graphs in the pattern.
25 = 02 + (±5)2 =
(±5)2 + 02 = (±3)2 +
(±4)2 = (±4)2 +
and this shows that there are 12 points with integer coordinates
on the circle x2+ y2 = 52 with
centre at the origin and radius 5 units.